Calculating the Mass of a Ball with F = 9.5 N and θ = 28°

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To calculate the mass of the ball with a horizontal force of 9.5 N at an angle of 28°, the sum of forces must equal zero, indicating equilibrium. The angle between the tension and the horizontal force is 118°, which helps in resolving the tension into vertical and horizontal components. The tension must balance the gravitational force acting on the ball, represented as mg, where m is the mass and g is the acceleration due to gravity. Using vector resolution and equilibrium principles, one can derive the mass of the ball from the tension components. A free body diagram (FBD) is recommended for clarity in calculations.
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Homework Statement


In the diagram below, the horizontal force, F, holds the ball steady. Given F = 9.5 N, and θ = 28°, calculate the mass of the ball. (I think I attached the picture, or well I hope I did)



Homework Equations


ƩF=ma



The Attempt at a Solution


So I know I have to find the angle between the two vectors, which is just 28°+90°=118°. Then I know the force from the tension must be equal to the horizontal force, I just can't seem to figure out the formula. I also think I need to find the hypotenuse, which is : 9.5 *Tan(118°)≈17.867 I think...

Well any help would be awesome, thanks for everything in advanced :)
 

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The resultant of forces in any direction is equal to zero.
Take any reference of frame for easy calculation.
Vectors in opposite or same direction can be added or substracted directly.
A vector can be resolved or replaced with 2 component vectors.

Finally draw a vector or fbd diagram.
 
Resolve the tension T in two vertical and horizontal components. Equate them to mg and F. From that find the required result.
 
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